Garagiola was a broadcaster for the D-backs from 1998-2012. His son, Joe Garagiola, Jr., is the former general manager of the D-backs and the current MLB senior vice president of standards and on-field operations.
In 2009, the broadcast wing and TV booth at Chase Field was named in Garagiola's honor.
"Joe was so special to everyone at the D-backs and had an aura about him that you could feel the moment you met him," D-backs president and CEO Derrick Hall said in a statement.
"Those of us who were lucky enough to know him personally were profoundly aware that the lovable personality that fans saw on TV was only surpassed by who he was in person and the way he treated everyone around him."
Garagiola became a household name during his broadcasting career. He was a panelist on The Today Show from 1966-73 and 1990-92 and was an occasional guest host of The Tonight Show.
He hosted several game shows, including Memory Game and To Tell the Truth, and he hosted the Westminster Kennel Club Dog Show from 1994-2002.
Garagiola was also politically active. He supported the re-election campaign of President Gerald Ford in 1976. In recent years, he advocated against the use of chewing tobacco.
In 2013, Garagiola received the Buck O'Neil Lifetime Achievement Award by the Baseball Hall of Fame for his contributions to pro baseball.
Garagiola is survived by his wife Audrie, three children and eight grandchildren. A funeral service will be held in Garagiola's hometown of St. Louis, and a local memorial will be held in Arizona at a later date, the D-backs announced.